Thermal Physics Physics 1X

1. Thermal PhysicsPhysics 1X Miles Padgett m.padgett@physics.gla.ac.uk

2. Thermodynamics • Understanding the words • Temperature • Heat • Heat capacity • The 0, 1, 2 laws of thermodynamics • (one of) Kelvin’s legacy’s WilliamThompson (Lord Kelvin)

3. I feel hot What is Heat? • Perception as to hot and cold defined relative to out own body temperature, i.e. object is hotter or colder than oneself • Objective measurement of temperature • Macroscopic, display of temperature gauge • Microscopic behaviour of atoms and molecules He is hot

4. Measuring temperature • Properties of materials change with temperature • Length • Volume • Resistance

5. Hotter things become longer • All(?) solids get bigger when they get hot • A 1 metre long bar heated by 1 degree gets bigger by • Steel ≈0.01 mm • Glass ≈ 0.001 mm • Zerodur ≈ 0.0001mm Rails expand and may buckle on a hot summer day

6. A bimetallic strip • Join two metals with different coefficient of thermal expansion e.g. fire alarm

7. Hotter things take up more volume -1 • Most materials get bigger when they get hot (but not water 0°C -> 4°C gets smaller!) • Thermometer relies on a thermal expansion of a liquid (e.g.mercury) Thin tube (Gives big length change for small increase in volume) Large volume of reservoir

8. Hotter things take up more volume -2 • Gases (as we will see) can behave near perfectly Hotter

9. Hotter things change their resistance • All hotter metals have a higher electrical resistance • e.g. platinum resistance thermometer • All hotter semiconductors have a lower electrical resistance • key definition between to distinguish metals and insulators!

10. How long do you have to leave a thermometer in your mouth? • Hot things stay hot if you insulate them, e.g. • coffee in a vacuum flask (keeps things cold too) • an explorer in a fur coat • The mercury in the thermometer must reach the same temperature and you

11. Insulation • Example of good (thermal) insulators • A vacuum, polystyrene, fibreglass, plastic, wood, brick • (low density/foam structure, poor electrical conductors) • Examples of poor insulators, i.e. good conductors • Most metals (but stainless steel better than copper) e.g. gold contact used within IC chips to prevent heating • Gases, liquids • (high density, “mobile”, good electrical conductors)

12. Ask a friend if it’s cool enough to eat • Your friend eats the “hot” loaf and says it cool enough to eat (i.e it is “close” enough to their own temperature that it does not burn) • Is it safe for you to eat too • If it is safe for then, it’s safe for you!

13. The 0th law of thermodynamics • If A and B are each in thermal equilibrium with C then A and B are in thermal equilibrium with each other • If Alfred and the Bread are the same temperature as Cliff then Alf is the same temperature as the Bread. =Temp =Temp? =Temp Cliff Alf

14. Temperature and scales • Temperature scales (melting & boiling of water) • Degrees Celsius (MP 0°C 100°C) • Degrees Kelvin (MP 273.15 K BP 373.15 K) • Degree Fahrenheit (MP 32° F BP 212°F)

15. Converting between scales • Kelvin to Celsius • K = C + 273.15 • C = K - 273.15 • Fahrenheit to Celsius • F = C x (9/5) + 32 • C = (F - 32) x (5/9)

16. Convert the following temperatures into °F and K Boiling water, 100°C Freezing water, 0°C Absolute zero, -273.15°C Example 212°F, 373.15K 32°F, 273.15K -460°F, 0K

17. Type of thermometer • Change in electrical resistance (convenient but not very linear) • Change in length of a bar (bimetallic strip) • Change in volume of a liquid • Change in volume of gas (very accurate but slow and bulky)

18. Volume and pressure of a gas • Gases (at constant pressure) expand with increasing temperature • all gases tend to zero volume at - 273.15°C! • Gases (at constant volume) increase pressure with increasing temperature • all gases tend to zero pressure at - 273.15°C! • In reality gases liquefy when they get cold pressure 0 100 -200 -100 200 temp. °C

19. Pressure • Pressure is defined as force per unit area • Newtons per square metre N/m2 • The pressure exerted by a gas results from the atoms/ molecules “bumping” into the container walls • More atoms gives more bumps and higher pressure • Higher temperature gives faster bumps and higher pressure • At sea level and 20°C, normal atmospheric pressure is • 1atm ≈ 1 x 105 N/m2

20. Volume and Pressure of a Gas • In the kelvin scale, the lowest possible temperature is 0 K. (zero volume and zero pressure) • Any two temperatures defined by the ratio • p1 T2 = p2 T1 or V1 T2 = V2 T1 • The zero point is fixed - • Absolution Zero (≈-273.15°C) • additional point defined at triple point of water (occurs at one temp and pressure where ice, steam and liquid all coexist (≈ 0.01°C and 0.006 atm) • Ttriple = 273.16K • T = 273.16 x (p/ptriple)

21. A bottle of hair spray is filled to a pressure of 1atm at 20°C What is the canister pressure if it is placed into boiling water? Example p1 T2 = p2 T1 1 x 373 = p2 x 293 p2 = 373/293 p2 = 1.27 atm

22. Absolute zero • Ideal gas has zero volume • Resistance of metal drops to zero (actually superconductivity cuts in above 0K) • Brownian motion ceases (kinetic energy due to thermal excitation ≈ 3/2 kT, see Physics 1Y) • But lowest temperature attained is ≈ 10-9K

23. How fast does a typical average gas atom/molecule travel at room temperature? (k = 1.38x10-23J/K) Example KE = 1/2 mv2 = 1/2 kT v = (kT/m)1/2 v = (1.38x10-23 x 293/m)1/2 m = 0.03/(6.023 x 1023)= 5x10-26 kg v = 284 sm/sec

24. Lord Kelvin • William Thompson, born Belfast 1824 • Student in Natural Philosophy • Professor at 22! • Baron Kelvin of Largs in 1897 • Lived at 11 The Square • A giant • Thermodynamics, Foams, Age of the Earth, Patents galore!

25. Thermal expansion, why? x • Every microscopic object moves due to thermal excitation - Brownian motion • Atoms too vibrate with respect to each other • Hotter atoms vibrate more • Asymmetric potential means average separation increases Potential energy between two atoms U(x) Average separation x High T Thermal excitation Low T

26. Linear expansion • Objects get longer when the get hot • Their fractional change in length is proportional to the change in temperature • DL/L = a DT or DL = a L DT • or L DL DL/L = aDT L DL DL/L = aDT

27. Thermal expansion (a[K-1]) • Aluminium, a = 2.4x10-5 K -1 • Steel, a = 1.2x10-5 K -1 • Glass, a ≈ 5 x10-6 K -1 • Invar, a ≈ 9 x10-7 K -1 • Quartz, a ≈ 4 x10-7 K -1

28. Metre rules are calibrated at 20°C What is the error in a measurement of 500mm if made at 45°C? asteel= 1.2x10-5 K-1 Example DL/L = aDT DL = L a DT DL = 500 x10-3 x 1.2x10-5 x 25 DL = 1.5x10-6m = 1.5µm

29. Volume Expansion • Every length goes from L to L+DL = L + La DT • Old volume = L3 • New volume = (L +DL)3 • Ignore terms like DL2 and DL3 • (L +DL)3 ≈ L3 + 3L2 DL • But DL = La DT • L3 + 3L2 DL = L3 + 3L3 aDT • DV/V = 3a DT or DL = 3a V DT • 3a often called b DL L

30. If whisky bottles are made to be exactly 1 litre at 20°C but, whisky is bottled at 10°C How much whisky do you actually get if it is served at 20°C? bglass= 2x10-5 K-1 bwhisky=75x10-5 K-1 Example Vbottle@10°C = Vbottle@20°C (1+ DTb) Vbottle@10°C = 1 (1+ -10 x 2x10-5) Vbottle@10°C = 0.9998 litres What does 0.9998 litres of whisky at 10°C occupy at 20°C? Vwhisky@20°C = Vwhisky@10°C (1 + DTb) Vwhisky@20°C = 0.9998 (1+10 x 2x10-5) Vwhisky@20°C = 0.9998 (1+10 x75x10-5) Vwhisky@20°C = 1.0073 litres

31. Shape change on expansion • This can be very complex for mis-matched materials • Single material (or matched a) much simpler bigger diameter bigger hole hotter

32. Thermal expansion solid-liquid-gas • Normally, density (r) changes as solid gas Density liquid Temperature

33. Thermal expansion of water • Density of ice is less than water!!! • Icebergs float • Density of water maximum at 4°C • Nearly frozen water floats to the top of the lake and hence freezes 1.0004 Density (kg/m3) 1.0002 1.0000 0 4 8 Temperature (°C)

34. How much energy required to heat object? • Heat (energy) flows because of temperature difference • Bigger temperature difference bigger heat flow • Less insulation give more heat flow for the same temperature difference • Heat will not flow between two bodies of the same temperature

35. Equilibrium • Two objects of different temperature when placed in contact will reach the same temperature + = Warm white coffee Hot black coffee Cold milk

36. Heat transfer = energy transfer • Energy measured in Joules but heat often measured in Calories • One cal raises one gram of water from 14.5°C to 15.5°C • 1 cal - 4.186J • Doing work on something usually makes it hot • Splash in the bath and the water will get warm! • 1st law of thermodynamics heat and work are both forms of energy

37. Sir James Joule • James Joule 1818-1889 • Stirring water made it warm • Change in temperature proportional to work done • Showing equivalence of heat and energy • Also that electrical current flow through a resistor gives heating

38. Some things are easier to heat (specific heat capacity) • More water in the kettle needs longer time to boil • Alcohol needs less energy to heat it than water • Energy required (Q) proportional desired change in temperature (DT) x mass (m) of material • Q = mc DT • c called the specific heat • cwater = 4190 J/(kg K) - very difficult to heat • cice = 2000 J/(kg K) • cmercury = 138 J/(kg K) - very easy to heat • cethanol = 2428 J/(kg K) - very easy to heat

39. “thrashing” around in the bath should heat up the water. How much will the water heat up after one minute of “thrashing” Example Estimate volume of water ≈ 0.5m3 Estimate power of thrashing ≈ 500W DT = Q/mcwater DT = 500 x 60 /500 x 4190 DT = 0.015°C

40. Molar heat capacity • Quote Joules per mole rather than Joules per kilogram • i.e. Q = nMc DT • n is the number of moles • Mc is the molar heat capacity (J/(mol K) • Mc ≈ 25 J/(mol K) for solids! • i.e. energy required to heat one atom of anything is about the same • Realised by Dulong and Petit

41. Phase changes (e.g. solid to liquid) • When heating ice into water and then into steam the temperature does not go up uniformly • Different gradients (cwater > cice ) • Flat bits at phase changes steam BP Temperature water MP ice time

42. Energy required for phase change • Heat of fusion (Q), solid -> liquid • Q = mLf (Lf is latent heat of fusion) • Lf (water) = 334 x103 J/kg • Lf (mercury) = 11.8 x103 J/kg • Heat of vapourisation (Q), liquid -> gas • Q = mLv (Lv is latent heat of vapourisation) • Lv (water) = 2256 x103 J/kg • Lv (mercury) = 272 x103 J/kg • Heat of sublimation (Q), solid -> gas • Q = mLs (Ls is latent heat of sublimation)

43. Using condensation to transfer energy • Steam has two contributions to its stored thermal energy • The energy it took to heat it to 100°C • The energy it took turn it from water at 100°C to steam at 100°C Turning water into steam is a thermally efficient way of cooling things down

44. If it takes 2 mins for your kettle to begin boiling how much longer does it take to boil dry? Assume kettle is 3kW Starting temp of water 20°C Example Work done by kettle = power x time = 2 x 60 x 3000 = 360 000J = Work to boil water of mass M = DT x M x cwater = 80 x M x 4190 = 335200 M -> Mass of water = 1.07kg Energy to boil water = M x Lv (water) = 1.07 x 2256 x103= 2420 000J Time required = Energy /power = 2420 000/3000 = 808 s ≈ 13mins

45. Reaching thermal equilibrium • Total energy (heat) of a closed system is constant, DQcoffee = -DQmilki.e S DQ =0 • By convention heat flowing into a body DQ +ve + = Hot black coffee at TH Cold milk at TC Warm white coffee at Tw (TH - Tw)mcoffeeccoffee = -(Tc - Tw)mmilkcmilk

46. Transferring heat energy • 3 mechanisms • Conduction • Heat transfer through material • Convection • Heat transfer by movement of hot material • Radiation • Heat transfer by light

47. Conduction of heat • Conduction in solids • Heat energy causes atoms to vibrate, a vibrating atom passes this vibration to the next • Conduction in metal • Heat energy causes electrons to gain energy, electrons travel through metal (conduction) and carry heat energy with them • Metals are good conductors of both heat and electricity

48. Rate of heat flow • Heat flow (H) is energy transfer per unit time, depends on • Temperature difference • Thermal conductivity (k) • k (copper) = 385 W/(m K) • k (glass) = 0.8 W/(m K) • k (air) =0.02 W/(m K) A TH TC L

49. You poke a 1.2m long, 10mm dia. copper bar into molten lead How much heat energy flows through the bar to you? Lead melts at 600K Example Temperature difference along rod DT = 600 - 311 = 289K H = kcopper A (DT/L) A=p x r2=3.142 x 0.0052 =0.000078m2 H = k A (DT/L) = 7.3 units? Units = {W/ (mK)} m2 K / m = Watts

50. Thermal conduction vs thermal resistance • Also can use thermal resistance, cf • Can make equation of heat flow more general